13-1
Chapter 13
Capital Budgeting
Techniques
13-2
Capital Budgeting
Techniques
? Project Evaluation and Selection
? Potential Difficulties
? Capital Rationing
? Project Monitoring
? Post-Completion Audit
13-3
Project Evaluation,
Alternative Methods
? Payback Period (PBP)
? Internal Rate of Return (IRR)
? Net Present Value (NPV)
? Profitability Index (PI)
13-4
Proposed Project Data
Julie Miller is evaluating a new project
for her firm Basket Wonders (BW),
She has determined that the after-tax
cash flows for the project will be
$10,000,$12,000,$15,000,$10,000,
and $7,000 respectively for each of
the Years 1 through 5,The initial
cash outlay will be $40,000.
13-5
Independent Project
?Independent -- A project whose
acceptance (or rejection) does not
prevent the acceptance of other
projects under consideration.
?For this project,assume that it is
independent of any other potential
projects that Basket Wonders may
undertake.
13-6
Payback Period (PBP)
PBP is the period of time
required for the cumulative
expected cash flows from an
investment project to equal
the initial cash outflow.
0 1 2 3 4 5
-40 K 10 K 12 K 15 K 10 K 7 K
13-7
(c)10 K 22 K 37 K 47 K 54 K
Payback Solution (#1)
PBP = a + ( b - c ) / d
= 3 + (40 - 37) / 10
= 3 + (3) / 10
= 3.3 Years
0 1 2 3 4 5
-40 K 10 K 12 K 15 K 10 K 7 K
Cumulative
Inflows
(a)
(-b) (d)
13-8
-40 K -30 K -18 K -3 K 7 K 14 K
Payback Solution (#2)
PBP = 3 + ( 3K ) / 10K
= 3.3 Years
Note,Take absolute value of last
negative cumulative cash flow
value.
0 1 2 3 4 5
-40 K 10 K 12 K 15 K 10 K 7 K
Cumulative
Cash Flows
13-9
PBP Acceptance Criterion
Yes! The firm will receive back the
initial cash outlay in less than 3.5
Years,[3.3 Years < 3.5 Year Max.]
The management of Basket Wonders
has set a maximum PBP of 3.5
Years for projects of this type.
Should this project be accepted?
13-10
PBP Strengths
and Weaknesses
Strengths:
? Easy to use and
understand
? Can be used as a
measure of
liquidity
? Easier to forecast
ST than LT flows
Weaknesses:
? Does not account
for TVM
? Does not consider
cash flows beyond
the PBP
? Cutoff period is
subjective
13-11
Internal Rate of Return (IRR)
IRR is the discount rate that equates the
present value of the future net cash
flows from an investment project with
the project’s initial cash outflow.
CF1 CF2 CFn
(1+IRR)1 (1+IRR)2 (1+IRR)n+,,, ++ICO =
13-12
$15,000 $10,000 $7,000
IRR Solution
$10,000 $12,000
(1+IRR)1 (1+IRR)2
Find the interest rate (IRR) that causes the
discounted cash flows to equal $40,000.
+ +
++$40,000 =
(1+IRR)3 (1+IRR)4 (1+IRR)5
13-13
IRR Solution (Try 10%)
$40,000 = $10,000(PVIF10%,1) + $12,000(PVIF10%,2) +
$15,000(PVIF10%,3) + $10,000(PVIF10%,4) +
$ 7,000(PVIF10%,5)
$40,000 = $10,000(.909) + $12,000(.826) +
$15,000(.751) + $10,000(.683) +
$ 7,000(.621)
$40,000 = $9,090 + $9,912 + $11,265 +
$6,830 + $4,347
= $41,444 [Rate is too low!!]
13-14
IRR Solution (Try 15%)
$40,000 = $10,000(PVIF15%,1) + $12,000(PVIF15%,2) +
$15,000(PVIF15%,3) + $10,000(PVIF15%,4) +
$ 7,000(PVIF15%,5)
$40,000 = $10,000(.870) + $12,000(.756) +
$15,000(.658) + $10,000(.572) +
$ 7,000(.497)
$40,000 = $8,700 + $9,072 + $9,870 +
$5,720 + $3,479
= $36,841 [Rate is too high!!]
13-15
.10 $41,444
.05 IRR $40,000 $4,603
.15 $36,841
X $1,444
.05 $4,603
IRR Solution (Interpolate)
$1,444X
=
13-16
.10 $41,444
.05 IRR $40,000 $4,603
.15 $36,841
X $1,444
.05 $4,603
IRR Solution (Interpolate)
$1,444X
=
13-17
.10 $41,444
.05 IRR $40,000 $4,603
.15 $36,841
($1,444)(0.05)
$4,603
IRR Solution (Interpolate)
$1,444X
X = X =,0157
IRR =,10 +,0157 =,1157 or 11.57%
13-18
IRR Acceptance Criterion
No! The firm will receive 11.57% for
each dollar invested in this project at
a cost of 13%,[ IRR < Hurdle Rate ]
The management of Basket Wonders
has determined that the hurdle rate
is 13% for projects of this type.
Should this project be accepted?
13-19
IRR Strengths
and Weaknesses
Strengths,
? Accounts for
TVM
? Considers all
cash flows
? Less
Subjectivity
Weaknesses,
? Assumes all cash
flows reinvested at
the IRR
? Difficulties with
project rankings and
Multiple IRRs
13-20
Net Present Value (NPV)
NPV is the present value of an
investment project’s net cash
flows minus the project’s initial
cash outflow.
CF1 CF2 CFn
(1+k)1 (1+k)2 (1+k)n+,,, ++ - ICONPV =
13-21
Basket Wonders has determined that the
appropriate discount rate (k) for this
project is 13%.
$10,000 $7,000
NPV Solution
$10,000 $12,000 $15,000
(1.13)1 (1.13)2 (1.13)3+ +
+ - $40,000(1.13)4 (1.13)5
NPV = +
13-22
NPV Solution
NPV = $10,000(PVIF13%,1) + $12,000(PVIF13%,2) +
$15,000(PVIF13%,3) + $10,000(PVIF13%,4) +
$ 7,000(PVIF13%,5) - $40,000
NPV = $10,000(.885) + $12,000(.783) +
$15,000(.693) + $10,000(.613) +
$ 7,000(.543) - $40,000
NPV = $8,850 + $9,396 + $10,395 +
$6,130 + $3,801 - $40,000
= - $1,428
13-23
NPV Acceptance Criterion
No! The NPV is negative,This means
that the project is reducing shareholder
wealth,[Reject as NPV < 0 ]
The management of Basket Wonders
has determined that the required
rate is 13% for projects of this type.
Should this project be accepted?
13-24
NPV Strengths
and Weaknesses
Strengths:
? Cash flows
assumed to be
reinvested at the
hurdle rate.
? Accounts for TVM.
? Considers all
cash flows.
Weaknesses:
? May not include
managerial
options embedded
in the project,See
Chapter 14.
13-25
Net Present Value Profile
Discount Rate (%)
0 3 6 9 12 15
IRR
NPV@13%
Sum of CFs Plot NPV for each
discount rate.
Ne
t P
re
se
nt
V
alu
e
$000s
15
10
5
0
-4
13-26
Profitability Index (PI)
PI is the ratio of the present value of
a project’s future net cash flows to
the project’s initial cash outflow.
CF1 CF2 CFn
(1+k)1 (1+k)2 (1+k)n+,,, ++ ICOPI =
PI = 1 + [ NPV / ICO ]
<< OR >>
13-27
PI Acceptance Criterion
No! The PI is less than 1.00,This
means that the project is not profitable,
[Reject as PI < 1.00 ]
PI = $38,572 / $40,000
=,9643
Should this project be accepted?
13-28
PI Strengths
and Weaknesses
Strengths:
? Same as NPV
? Allows
comparison of
different scale
projects
Weaknesses:
? Same as NPV
? Provides only
relative profitability
? Potential Ranking
Problems
13-29
Evaluation Summary
Me th o d Pro je ct Co mp ari so n Dec is io n
PBP 3,3 3,5 Acc ep t
IR R 11,57% 13% Rej ect
NP V -$1,4 28 $0 Rej ect
PI,9 6 1,00 Rej ect
Basket Wonders Independent Project
13-30
Other Project
Relationships
?Mutually Exclusive -- A project
whose acceptance precludes the
acceptance of one or more
alternative projects,
?Dependent -- A project whose
acceptance depends on the
acceptance of one or more other
projects.
13-31
Potential Problems
Under Mutual
Exclusivity
A,Scale of Investment
B,Cash-flow Pattern
C,Project Life
Ranking of project proposals may
create contradictory results.
13-32
A,Scale Differences
Compare a small (S) and a
large (L) project.
NET CASH FLOWS
Project S Project LEND OF YEAR
0 -$100 -$100,000
1 0 0
2 $400 $156,250
13-33
S,50 Yrs 100% $231 3.31
L 1.28 Yrs 25% $29,132 1.29
Scale Differences
Calculate the PBP,IRR,NPV@10%,
and PI@10%.
Which project is preferred? Why?
Project PBP IRR NPV PI
13-34
B,Cash Flow Pattern
Let us compare a decreasing cash-flow (D)
project and an increasing cash-flow (I) project.
NET CASH FLOWS
Project D Project IEND OF YEAR
0 -$1,200 -$1,200
1 1,000 100
2 500 600
3 100 1,080
13-35
D 23% $198 1.17
I 17% $198 1.17
Cash Flow Pattern
Calculate the IRR,NPV@10%,
and PI@10%.
Which project is preferred?
Project IRR NPV PI
13-36
Examine NPV Profile
Discount Rate (%)
0 5 10 15 20 25-20
0
0
20
0
4
00
6
00
IRR
NPV@10%
Plot NPV for each
project at various
discount rates.
Ne
t P
re
se
nt
V
alu
e (
$)
13-37
Fisher’s Rate of Intersection
Discount Rate ($)
0 5 10 15 20 25-20
0
0
20
0
4
00
6
00
Ne
t P
re
se
nt
V
alu
e (
$)
At k<10%,I is best!
Fisher’s Rate of
Intersection
At k>10%,D is best!
13-38
C,Project Life Differences
Let us compare a long life (X) project
and a short life (Y) project.
NET CASH FLOWS
Project X Project YEND OF YEAR
0 -$1,000 -$1,000
1 0 2,000
2 0 0
3 3,375 0
13-39
X,89 Yrs 50% $1,536 2.54
Y,50 Yrs 100% $818 1.82
Project Life Differences
Calculate the PBP,IRR,NPV@10%,
and PI@10%.
Which project is preferred? Why?
Project PBP IRR NPV PI
13-40
Another Way to
Look at Things
1,Adjust cash flows to a common terminal
year if project will not be replaced.
Compound Project Y,Year 1 @10% for 2 years.
Year 0 1 2 3
CF -$1,000 $0 $0 $2,420
Results,IRR* = 34.26% NPV = $818
*Lower IRR from adjusted cash-flow stream,X is still Best.
13-41
Replacing Projects
with Identical Projects
2,Use Replacement Chain Approach
when project will be replaced.
0 1 2 3
-$1,000 $2,000
-1,000 $2,000
-1,000 $2,000
-$1,000 $1,000 $1,000 $2,000
Results,IRR* = 100% NPV = $2,238.17
*Lower IRR from adjusted cash flow stream,Y is Best.
13-42
Capital Rationing
Capital Rationing occurs when a
constraint (or budget ceiling) is placed
on the total size of capital expenditures
during a particular period.
Example
Julie Miller must determine what
investment opportunities to undertake for
Basket Wonders (BW),She is limited to a
maximum expenditure of $32,500 only for
199X.
13-43
Available Projects for BW
Project ICO IRR NPV PI
A $ 500 18% $ 50 1.10
B 5,000 25 6,500 2.30
C 5,000 37 5,500 2.10
D 7,500 20 5,000 1.67
E 12,500 26 500 1.04
F 15,000 28 21,000 2.40
G 17,500 19 7,500 1.43
H 25,000 15 6,000 1.24
13-44
Choosing by IRRs for BW
Project ICO IRR NPV PI
C $ 5,000 37% $ 5,500 2.10
F 15,000 28 21,000 2.40
E 12,500 26 500 1.04
B 5,000 25 6,500 2.30
Projects C,F,and E have the
three largest IRRs.
The resulting increase in shareholder wealth
is $27,000 with a $32,500 outlay.
13-45
Choosing by NPVs for BW
Project ICO IRR NPV PI
F $15,000 28% $21,000 2.40
G 17,500 19 7,500 1.43
B 5,000 25 6,500 2.30
Projects F and G have the
two largest NPVs.
The resulting increase in shareholder
wealth is $28,500 with a $32,500 outlay.
13-46
Choosing by PIs for BW
Project ICO IRR NPV PI
F $15,000 28% $21,000 2.40
B 5,000 25 6,500 2.30
C 5,000 37 5,500 2.10
D 7,500 20 5,000 1.67
G 17,500 19 7,500 1.43
Projects F,B,C and D have the four largest PIs.
The resulting increase in shareholder wealth is
$38,000 with a $32,500 outlay.
13-47
Summary of Comparison
Method Projects Accepted Value Added
PI F,B,C,and D $38,000
NPV F and G $28,500
IRR C,F and E $27,000
PI generates the greatest increase in
shareholder wealth when a limited capital
budget exists for a single period.
13-48
Post-Completion Audit
Post-completion Audit
A formal comparison of the actual costs and
benefits of a project with original estimates.
? Identify any project weaknesses
? Develop a possible set of corrective actions
? Provide appropriate feedback
Result,Making better future decisions!
13-49
Multiple IRR Problem
Two!! There are as many potential
IRRs as there are sign changes.
Let us assume the following cash flow
pattern for a project for Years 0 to 4:
-$100 +$100 +$900 -$1,000
How many potential IRRs could this
project have?
13-50
NPV Profile -- Multiple IRRs
Discount Rate (%)
0 40 80 120 160 200
Ne
t P
re
se
nt
V
alu
e
($
00
0s
)
Multiple IRRs at
k = 12.95% and 191.15%
75
50
25
0
-100
Chapter 13
Capital Budgeting
Techniques
13-2
Capital Budgeting
Techniques
? Project Evaluation and Selection
? Potential Difficulties
? Capital Rationing
? Project Monitoring
? Post-Completion Audit
13-3
Project Evaluation,
Alternative Methods
? Payback Period (PBP)
? Internal Rate of Return (IRR)
? Net Present Value (NPV)
? Profitability Index (PI)
13-4
Proposed Project Data
Julie Miller is evaluating a new project
for her firm Basket Wonders (BW),
She has determined that the after-tax
cash flows for the project will be
$10,000,$12,000,$15,000,$10,000,
and $7,000 respectively for each of
the Years 1 through 5,The initial
cash outlay will be $40,000.
13-5
Independent Project
?Independent -- A project whose
acceptance (or rejection) does not
prevent the acceptance of other
projects under consideration.
?For this project,assume that it is
independent of any other potential
projects that Basket Wonders may
undertake.
13-6
Payback Period (PBP)
PBP is the period of time
required for the cumulative
expected cash flows from an
investment project to equal
the initial cash outflow.
0 1 2 3 4 5
-40 K 10 K 12 K 15 K 10 K 7 K
13-7
(c)10 K 22 K 37 K 47 K 54 K
Payback Solution (#1)
PBP = a + ( b - c ) / d
= 3 + (40 - 37) / 10
= 3 + (3) / 10
= 3.3 Years
0 1 2 3 4 5
-40 K 10 K 12 K 15 K 10 K 7 K
Cumulative
Inflows
(a)
(-b) (d)
13-8
-40 K -30 K -18 K -3 K 7 K 14 K
Payback Solution (#2)
PBP = 3 + ( 3K ) / 10K
= 3.3 Years
Note,Take absolute value of last
negative cumulative cash flow
value.
0 1 2 3 4 5
-40 K 10 K 12 K 15 K 10 K 7 K
Cumulative
Cash Flows
13-9
PBP Acceptance Criterion
Yes! The firm will receive back the
initial cash outlay in less than 3.5
Years,[3.3 Years < 3.5 Year Max.]
The management of Basket Wonders
has set a maximum PBP of 3.5
Years for projects of this type.
Should this project be accepted?
13-10
PBP Strengths
and Weaknesses
Strengths:
? Easy to use and
understand
? Can be used as a
measure of
liquidity
? Easier to forecast
ST than LT flows
Weaknesses:
? Does not account
for TVM
? Does not consider
cash flows beyond
the PBP
? Cutoff period is
subjective
13-11
Internal Rate of Return (IRR)
IRR is the discount rate that equates the
present value of the future net cash
flows from an investment project with
the project’s initial cash outflow.
CF1 CF2 CFn
(1+IRR)1 (1+IRR)2 (1+IRR)n+,,, ++ICO =
13-12
$15,000 $10,000 $7,000
IRR Solution
$10,000 $12,000
(1+IRR)1 (1+IRR)2
Find the interest rate (IRR) that causes the
discounted cash flows to equal $40,000.
+ +
++$40,000 =
(1+IRR)3 (1+IRR)4 (1+IRR)5
13-13
IRR Solution (Try 10%)
$40,000 = $10,000(PVIF10%,1) + $12,000(PVIF10%,2) +
$15,000(PVIF10%,3) + $10,000(PVIF10%,4) +
$ 7,000(PVIF10%,5)
$40,000 = $10,000(.909) + $12,000(.826) +
$15,000(.751) + $10,000(.683) +
$ 7,000(.621)
$40,000 = $9,090 + $9,912 + $11,265 +
$6,830 + $4,347
= $41,444 [Rate is too low!!]
13-14
IRR Solution (Try 15%)
$40,000 = $10,000(PVIF15%,1) + $12,000(PVIF15%,2) +
$15,000(PVIF15%,3) + $10,000(PVIF15%,4) +
$ 7,000(PVIF15%,5)
$40,000 = $10,000(.870) + $12,000(.756) +
$15,000(.658) + $10,000(.572) +
$ 7,000(.497)
$40,000 = $8,700 + $9,072 + $9,870 +
$5,720 + $3,479
= $36,841 [Rate is too high!!]
13-15
.10 $41,444
.05 IRR $40,000 $4,603
.15 $36,841
X $1,444
.05 $4,603
IRR Solution (Interpolate)
$1,444X
=
13-16
.10 $41,444
.05 IRR $40,000 $4,603
.15 $36,841
X $1,444
.05 $4,603
IRR Solution (Interpolate)
$1,444X
=
13-17
.10 $41,444
.05 IRR $40,000 $4,603
.15 $36,841
($1,444)(0.05)
$4,603
IRR Solution (Interpolate)
$1,444X
X = X =,0157
IRR =,10 +,0157 =,1157 or 11.57%
13-18
IRR Acceptance Criterion
No! The firm will receive 11.57% for
each dollar invested in this project at
a cost of 13%,[ IRR < Hurdle Rate ]
The management of Basket Wonders
has determined that the hurdle rate
is 13% for projects of this type.
Should this project be accepted?
13-19
IRR Strengths
and Weaknesses
Strengths,
? Accounts for
TVM
? Considers all
cash flows
? Less
Subjectivity
Weaknesses,
? Assumes all cash
flows reinvested at
the IRR
? Difficulties with
project rankings and
Multiple IRRs
13-20
Net Present Value (NPV)
NPV is the present value of an
investment project’s net cash
flows minus the project’s initial
cash outflow.
CF1 CF2 CFn
(1+k)1 (1+k)2 (1+k)n+,,, ++ - ICONPV =
13-21
Basket Wonders has determined that the
appropriate discount rate (k) for this
project is 13%.
$10,000 $7,000
NPV Solution
$10,000 $12,000 $15,000
(1.13)1 (1.13)2 (1.13)3+ +
+ - $40,000(1.13)4 (1.13)5
NPV = +
13-22
NPV Solution
NPV = $10,000(PVIF13%,1) + $12,000(PVIF13%,2) +
$15,000(PVIF13%,3) + $10,000(PVIF13%,4) +
$ 7,000(PVIF13%,5) - $40,000
NPV = $10,000(.885) + $12,000(.783) +
$15,000(.693) + $10,000(.613) +
$ 7,000(.543) - $40,000
NPV = $8,850 + $9,396 + $10,395 +
$6,130 + $3,801 - $40,000
= - $1,428
13-23
NPV Acceptance Criterion
No! The NPV is negative,This means
that the project is reducing shareholder
wealth,[Reject as NPV < 0 ]
The management of Basket Wonders
has determined that the required
rate is 13% for projects of this type.
Should this project be accepted?
13-24
NPV Strengths
and Weaknesses
Strengths:
? Cash flows
assumed to be
reinvested at the
hurdle rate.
? Accounts for TVM.
? Considers all
cash flows.
Weaknesses:
? May not include
managerial
options embedded
in the project,See
Chapter 14.
13-25
Net Present Value Profile
Discount Rate (%)
0 3 6 9 12 15
IRR
NPV@13%
Sum of CFs Plot NPV for each
discount rate.
Ne
t P
re
se
nt
V
alu
e
$000s
15
10
5
0
-4
13-26
Profitability Index (PI)
PI is the ratio of the present value of
a project’s future net cash flows to
the project’s initial cash outflow.
CF1 CF2 CFn
(1+k)1 (1+k)2 (1+k)n+,,, ++ ICOPI =
PI = 1 + [ NPV / ICO ]
<< OR >>
13-27
PI Acceptance Criterion
No! The PI is less than 1.00,This
means that the project is not profitable,
[Reject as PI < 1.00 ]
PI = $38,572 / $40,000
=,9643
Should this project be accepted?
13-28
PI Strengths
and Weaknesses
Strengths:
? Same as NPV
? Allows
comparison of
different scale
projects
Weaknesses:
? Same as NPV
? Provides only
relative profitability
? Potential Ranking
Problems
13-29
Evaluation Summary
Me th o d Pro je ct Co mp ari so n Dec is io n
PBP 3,3 3,5 Acc ep t
IR R 11,57% 13% Rej ect
NP V -$1,4 28 $0 Rej ect
PI,9 6 1,00 Rej ect
Basket Wonders Independent Project
13-30
Other Project
Relationships
?Mutually Exclusive -- A project
whose acceptance precludes the
acceptance of one or more
alternative projects,
?Dependent -- A project whose
acceptance depends on the
acceptance of one or more other
projects.
13-31
Potential Problems
Under Mutual
Exclusivity
A,Scale of Investment
B,Cash-flow Pattern
C,Project Life
Ranking of project proposals may
create contradictory results.
13-32
A,Scale Differences
Compare a small (S) and a
large (L) project.
NET CASH FLOWS
Project S Project LEND OF YEAR
0 -$100 -$100,000
1 0 0
2 $400 $156,250
13-33
S,50 Yrs 100% $231 3.31
L 1.28 Yrs 25% $29,132 1.29
Scale Differences
Calculate the PBP,IRR,NPV@10%,
and PI@10%.
Which project is preferred? Why?
Project PBP IRR NPV PI
13-34
B,Cash Flow Pattern
Let us compare a decreasing cash-flow (D)
project and an increasing cash-flow (I) project.
NET CASH FLOWS
Project D Project IEND OF YEAR
0 -$1,200 -$1,200
1 1,000 100
2 500 600
3 100 1,080
13-35
D 23% $198 1.17
I 17% $198 1.17
Cash Flow Pattern
Calculate the IRR,NPV@10%,
and PI@10%.
Which project is preferred?
Project IRR NPV PI
13-36
Examine NPV Profile
Discount Rate (%)
0 5 10 15 20 25-20
0
0
20
0
4
00
6
00
IRR
NPV@10%
Plot NPV for each
project at various
discount rates.
Ne
t P
re
se
nt
V
alu
e (
$)
13-37
Fisher’s Rate of Intersection
Discount Rate ($)
0 5 10 15 20 25-20
0
0
20
0
4
00
6
00
Ne
t P
re
se
nt
V
alu
e (
$)
At k<10%,I is best!
Fisher’s Rate of
Intersection
At k>10%,D is best!
13-38
C,Project Life Differences
Let us compare a long life (X) project
and a short life (Y) project.
NET CASH FLOWS
Project X Project YEND OF YEAR
0 -$1,000 -$1,000
1 0 2,000
2 0 0
3 3,375 0
13-39
X,89 Yrs 50% $1,536 2.54
Y,50 Yrs 100% $818 1.82
Project Life Differences
Calculate the PBP,IRR,NPV@10%,
and PI@10%.
Which project is preferred? Why?
Project PBP IRR NPV PI
13-40
Another Way to
Look at Things
1,Adjust cash flows to a common terminal
year if project will not be replaced.
Compound Project Y,Year 1 @10% for 2 years.
Year 0 1 2 3
CF -$1,000 $0 $0 $2,420
Results,IRR* = 34.26% NPV = $818
*Lower IRR from adjusted cash-flow stream,X is still Best.
13-41
Replacing Projects
with Identical Projects
2,Use Replacement Chain Approach
when project will be replaced.
0 1 2 3
-$1,000 $2,000
-1,000 $2,000
-1,000 $2,000
-$1,000 $1,000 $1,000 $2,000
Results,IRR* = 100% NPV = $2,238.17
*Lower IRR from adjusted cash flow stream,Y is Best.
13-42
Capital Rationing
Capital Rationing occurs when a
constraint (or budget ceiling) is placed
on the total size of capital expenditures
during a particular period.
Example
Julie Miller must determine what
investment opportunities to undertake for
Basket Wonders (BW),She is limited to a
maximum expenditure of $32,500 only for
199X.
13-43
Available Projects for BW
Project ICO IRR NPV PI
A $ 500 18% $ 50 1.10
B 5,000 25 6,500 2.30
C 5,000 37 5,500 2.10
D 7,500 20 5,000 1.67
E 12,500 26 500 1.04
F 15,000 28 21,000 2.40
G 17,500 19 7,500 1.43
H 25,000 15 6,000 1.24
13-44
Choosing by IRRs for BW
Project ICO IRR NPV PI
C $ 5,000 37% $ 5,500 2.10
F 15,000 28 21,000 2.40
E 12,500 26 500 1.04
B 5,000 25 6,500 2.30
Projects C,F,and E have the
three largest IRRs.
The resulting increase in shareholder wealth
is $27,000 with a $32,500 outlay.
13-45
Choosing by NPVs for BW
Project ICO IRR NPV PI
F $15,000 28% $21,000 2.40
G 17,500 19 7,500 1.43
B 5,000 25 6,500 2.30
Projects F and G have the
two largest NPVs.
The resulting increase in shareholder
wealth is $28,500 with a $32,500 outlay.
13-46
Choosing by PIs for BW
Project ICO IRR NPV PI
F $15,000 28% $21,000 2.40
B 5,000 25 6,500 2.30
C 5,000 37 5,500 2.10
D 7,500 20 5,000 1.67
G 17,500 19 7,500 1.43
Projects F,B,C and D have the four largest PIs.
The resulting increase in shareholder wealth is
$38,000 with a $32,500 outlay.
13-47
Summary of Comparison
Method Projects Accepted Value Added
PI F,B,C,and D $38,000
NPV F and G $28,500
IRR C,F and E $27,000
PI generates the greatest increase in
shareholder wealth when a limited capital
budget exists for a single period.
13-48
Post-Completion Audit
Post-completion Audit
A formal comparison of the actual costs and
benefits of a project with original estimates.
? Identify any project weaknesses
? Develop a possible set of corrective actions
? Provide appropriate feedback
Result,Making better future decisions!
13-49
Multiple IRR Problem
Two!! There are as many potential
IRRs as there are sign changes.
Let us assume the following cash flow
pattern for a project for Years 0 to 4:
-$100 +$100 +$900 -$1,000
How many potential IRRs could this
project have?
13-50
NPV Profile -- Multiple IRRs
Discount Rate (%)
0 40 80 120 160 200
Ne
t P
re
se
nt
V
alu
e
($
00
0s
)
Multiple IRRs at
k = 12.95% and 191.15%
75
50
25
0
-100
